Model Domains in C^3 with abelian automorphism group

TL;DR

This paper classifies certain hyperbolic polynomial domains in complex three-dimensional space with abelian automorphism groups, showing they are equivalent to balanced domains under some weight, advancing understanding of their structure.

Contribution

It proves that all hyperbolic rigid polynomial domains in C^3 with abelian automorphism groups are equivalent to weighted balanced domains, providing a classification result.

Findings

Domains are equivalent to weighted balanced domains

Automorphism groups are abelian

Classification of hyperbolic rigid polynomial domains

Abstract

It is shown that every hyperbolic rigid polynomial domain in C^3 of finite type, with abelian automorphism group is equivalent to a domain that is balanaced with respect to some weight.